/* www-ATLAS of Group Representations. U3(4) represented as 75 x 75 matrices over GF(3). */ F:=GF(3); x:=CambridgeMatrix(1,F,75,[ "010000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000", "212121000001002000100000000000000000000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000", "000000000000000000000000000000000000000000000000001000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000001000000000000000000000", "021010000002000000200000000000000000000000200000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000010000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000010", "222211121221021100011000102001020211010220011121202100210222102000100020020", "000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000", "101011120222121000212000110020221111101101220022120202001010101102012211120", "000000000000000000000000000000000000000000000000100000000000000000000000000", "120110021000122112112212210102112202001020021122111021210000020222000000221", "000010111202220211002000121212110120000101212122211010210111201111102211221", "220020121111220202022200112000220210121101111202001112011121201211021112202", "000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000000000000000000000000010000000000000000000000", "202012100120211201121201011122122210002222110021111202222122010220100122111", "210211021020211020201220120122210211202120012022222201201200021022210200011", "000000000000000000000000000000000000000000000000000000100000000000000000000", "210212112112212001211110120101122221112211100201210110220022222201001111010", "000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000", "021002210012221011221021101101112002202212221202100012110010022110112211101"]); y:=CambridgeMatrix(1,F,75,[ "001000000000000000000000000000000000000000000000000000000000000000000000000", "022000000000000000000000000000000000000000000000000000000000000000000000000", "121000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000", 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"000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000010000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000", "000000000000000000000000000000000000000000000000100000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000100000000000000000000", "000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000001000000", "000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000100000000000000000000000000000000000000000", "122122212112012000022000201002010112020110022212101200120111201000200010010", "111200220001000021200212121221010011000102120200111121120200220200201022210", "000000000000000000000000000000000000000000000000000000000000000000000000001", "212011022021010121020121022021200212120211202210102221011011101220102002101", "000000000000000000000000000000000000100000000000000000000000000000000000000", "201120211202200201220120212121020120121210020220210001021202221201012120022", "000000000000000000000000000000000000010000000000000000000000000000000000000", "100200020111022020210022001011101200220012120120101111000001012121111111010", "102222120112100220201222201021201000201201210020221122022210000101210200101", "102200210220100220120110020102101122221220022111020021222101120101021002112", "021222211020110012101212220222011211112111112001012100001000220121121122110", "000000000000000000000000000000000000000010000000000000000000000000000000000", "222122000102222111002111102100220222010001211211001120001200220020220010011", "222021020202122022001021022210200002001022122002202111112101020211211000222", "200011021012102022212022001112021010121201021002100022012000111122200220000", "022121220210021001201202100012112002001202001012012220212210012001000111002", "100200012021012200212211100102200112200022021000201002221211202211102210111", "010221122101010222011100210202210022202121012002100211120122122110210001010"]); G:=MatrixGroup<75,F|x,y>; print "Group G is U3(4) < GL(75,GF(3))";